[AccessD] bust out the math books

Scott Marcus marcus at tsstech.com
Wed Jan 25 15:31:24 CST 2006


Jim,

The problem is not a rounding error. The real average and the average of
averages are two distinct values. If they equal, it is only by
coincidence.

Scott Marcus

-----Original Message-----
From: accessd-bounces at databaseadvisors.com
[mailto:accessd-bounces at databaseadvisors.com] On Behalf Of Jim Lawrence
Sent: Wednesday, January 25, 2006 10:25 AM
To: 'Access Developers discussion and problem solving'
Subject: Re: [AccessD] bust out the math books

Hi Scott:

There must be a round off error somewhere in the process. As I am just
finishing off an accounting system this problem has always been
apparent.
There are a few ways that accounting applications resolve the round off
error.

1. Store all values as integers and perform any math using those
integers.
Example (assuming 6 significant places are required.) 

Value 0.884746 would become 884746 with a mantissa of 6. All subsequent
calculations are performed in integer math or logs are used. (Adding
instead
of multiple and subtract instead of dividing.)

2. In the case of a multiplication or division being required the
calculation is performed once and then the values are managed again as
integers. This is particularly true when applying taxes to invoicing.
Example (given that the state or provincial tax is 6.5% and the federal
tax
is 7.0%.)

The taxes are applied immediately then added from there on. In
appropriate
tax is generated per item: 

Given:
Subtotal 	PST		GST		Displayed/Saved Total
123.56	8.0314	8.6492 	
		8.03		8.65		140.24	
456.23	29.65495	31.9361
  		29.66		31.94		61.60
+
579.79	+37.69	+ 40.59	=658.07	right-way

579.79	* 1.135% (total tax)	=658.06	wrong-way

When tax totals are generated then all the tax subtotals are just added
together. In theory, all the subtotals could be added and the total tax
could be calculated but the answer would be wrong. This is the same
problem
experience when trying to calculate the average by item and then
expecting
the average for the whole group to add up. It never will.

HTH
Jim


-----Original Message-----
From: accessd-bounces at databaseadvisors.com
[mailto:accessd-bounces at databaseadvisors.com] On Behalf Of Scott Marcus
Sent: January 25, 2006 4:51 AM
To: Access Developers discussion and problem solving
Subject: Re: [AccessD] bust out the math books

Mathematical answer...

C1 = Total
C2 = Sample Size
C3 = Average

C1  C2  C3
===========
A   B   A/B
C   D   C/D
E   F   E/F
G   H   G/H
I   J   I/J


Real average = (A+C+E+G+I)/BDFHJ

Average of averages = (A/B + C/D + E/F + G/H + I/J)/5

Which equals...
((ADFHJ+CBFHJ+EBDHJ+GBDFJ+IBDFH)/(BDFHJ))/5
                    

Which equals...
(ADFHJ+CBFHJ+EBDHJ+GBDFJ+IBDFH)/5BDFHJ


(A+C+E+G+I)/BDFHJ does not equal 
(ADFHJ+CBFHJ+EBDHJ+GBDFJ+IBDFH)/5BDFHJ


Scott Marcus                   

-----Original Message-----
From: accessd-bounces at databaseadvisors.com
[mailto:accessd-bounces at databaseadvisors.com] On Behalf Of Francisco
Tapia
Sent: Tuesday, January 24, 2006 7:50 PM
To: Access Developers discussion and problem solving
Subject: [AccessD] bust out the math books

can someone answer me this:
  C1 C2
C3  1566 1770
0.884746  5130 5340
0.960674  1320 1800
0.733333  6440 7280
0.884615  1770 1800
0.983333



 16226 17990
0.901946
If I take C1 / C2 I get C3... there must be a mathimaticall reason as to
why
I can't just average column C3 to get the 90%, instead I end up with
88.93%

any thoughts?

--
-Francisco
http://pcthis.blogspot.com |PC news with out the jargon!
http://sqlthis.blogspot.com | Tsql and More...
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